Download Section 2 – 5 HW: Solving For Variables In Formulas Selected

Section 2 – 5 HW:
Solving For Variables In Formulas
Selected Worked Homework Problems
Solving Equations for a given Variable in a Formula
1. If the is a fraction in the equation, Multiply each term of the equation by the Lowest Common
Denominator (LCD). This will give you an equation without any fractions.
2. Distribute if there is a distribute operation in the equation.
3. Find the side of the equation with the variable you want to solve for. Add or subtract all the terms
without that variable from both sides of the equation to eliminate them from the side with the
variable.
4. Divide both sides of the equation by any factors multiplied with the variable.
5. If there is a negative sign in the denominator multiply the numerator and denominator by –1.
1.
Solve for M
A = 3B + 2M
2.
!
Solve for r
d = rt
!
!
Solve for M
Get the term 2M alone on thr right side
by subtracting 3B from both sides
Solve for r
Get the variable r alone on the right side
by dividing both sides by t
A = 3B + 2M add 3B to both sides
−3B − 3B
d r • t/
=
t
t
!
A − 3B = 2M
Divide both sides by 2
d
=r
t
A − 3B
2/ M
=
2
2/
A − 3B
=M
2
Math 100 !
Section 2–5 HW WKD
! © 2016 Eitel
3.
4.
Solve for L
!
P = 2L + 2W
Solve for L
Get the term 2L alone on the right side
by subtracting 2W from both sides
Solve for b
Get the term b alone on the right side
by subtracting mx from both sides
P = 2L + 2W
−2W
Solve for b
y = mx + b
y = mx + b
−m − mx
− 2W
!
P − 2W = 2L
Divide both sides by 2
y − mx = b
/
P − 2W 2L
=
2
2/
P − 2W
=L
2
5.
Solve for r
I = p rt
6.
!
Solve for r
Get the variable r alone on the right side
by dividing both sides by p and t
!
I
p • r • t/
=
p• t
p• t
Solve for b
P = a+b+c
Solve for b
Get the term b alone on the right side
by subtracting a and c from both sides
P = a + b + c
− a−c − a
−c
P − a−c = b
I
=r
pt
Math 100 !
Section 2–5 HW WKD
! © 2016 Eitel
7.
Solve for x
6x + 5y = 12
8.
!
4 x + 3y = 9
− 4x
− 4x
6x + 5y = 12
− 5y
6 x = −5y + 12
!
3y = −4 x + 9
Divide both sides by 6
Divide both sides by 3
6/ x −5y + 12
=
6/
6
3/ x
−4 x + 9
=
3/
3
x=
−5y + 12
6
Math 100 !
!
Solve for y
Get the term 3y alone on the right side
by subtracting 4x from both sides
Solve for x
Get the term 6x alone on the right side
by subtracting 5y from both sides
− 5y
Solve for y
4 x + 3y = 9
y =
−4 x + 9
3
Section 2–5 HW WKD
! © 2016 Eitel
11.
Solve for h
1 !
A = bh
2
12.
Solve for T
2T + m
A=
7
Solve for T
There is a fraction in the equation.
Eliminate the denominator by
multipling both sides by 7.
Solve for h
There is a fraction in the equation.
Eliminate the denominator by
multipling both sides by 2.
A = 7•
1
2 • A = 2/ • b • h
2/
2A = b • h
Get the variable b alone on the right side !
by divding both sides by b
2A
b/ • h
=
b
b/
2A
=h
b
Math 100 !
2T + m
7
7A = 2T + m
Get the 2T term alone on the right side
by subtraction m from both sides.
7A = 2T + m
−m
−m
7A − m = 2T
divide both sides by 2
7A − m
=T
2
Section 2–5 HW WKD
! © 2016 Eitel
13.
Solve for g
1
V = gt2
2
15.
!
Solve for A
There is a fraction in the equation.
Eliminate the denominator by
multipling both sides by 2.
Solve for g
There is a fraction in the equation.
Eliminate the denominator by
multipling both sides by 2.
2
3• F = 3/ • (A − B)
3/
1
2 • V = 2/ • g t 2
2/
3F = 2(A − B)
Distrubute the 2
2
2V = g • t
Get the variable g alone on the right side
by divding both sides by t 2
2V
=
t2
2V
t2
g• t2
t2
=g
Solve for A
2
F = (A − B)
3
!
3F = 2A − 2B
Get the 2A term alone on the right side
by adding 2B to both sides,
3F = 2A − 2B
+2B
+ 2B
3F + 2B = 2A
divide both sides by2
3F + 2B
=A
2
Math 100 !
Section 2–5 HW WKD
! © 2016 Eitel
27.
26.
Solve for y
3
x = y+6
2
There is a fraction in the equation.
Eliminate the denominator by
multipling EVETY TERM BY 2.
!
Solve for y
!
y 5
x= +
3 6
There is a fraction in the equation.
Eliminate the denominator by
multipling EVETY TERM BY 6.
3
2• x = 2• y + 2• 6
2
6• x = 6•
y
5
+ 6•
3
6
2x = 3y + 12
Get the 3y term alone on the right side
by subtracting 12 from both sides.
6x = 2y + 5
Get the 2y term alone on the right side
by subtracting 5 from both sides.
!
2x = 3y + 12
−12
− 12
6x = 2y + 5
−5
−5
2x − 12 = 3y
divide both sides by 2
6x − 5 = 2y
divide both sides by 2
2x − 12
=y
3
6x − 5
=y
2
Note: Do not try to reduce this answer.
Note: Do not try to reduce this answer.
Math 100 !
Section 2–5 HW WKD
! © 2016 Eitel